Q: What are the factor combinations of the number 655,722?

 A:
Positive:   1 x 6557222 x 3278613 x 2185746 x 1092879 x 7285818 x 3642927 x 2428654 x 12143
Negative: -1 x -655722-2 x -327861-3 x -218574-6 x -109287-9 x -72858-18 x -36429-27 x -24286-54 x -12143


How do I find the factor combinations of the number 655,722?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 655,722, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 655,722
-1 -655,722

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 655,722.

Example:
1 x 655,722 = 655,722
and
-1 x -655,722 = 655,722
Notice both answers equal 655,722

With that explanation out of the way, let's continue. Next, we take the number 655,722 and divide it by 2:

655,722 ÷ 2 = 327,861

If the quotient is a whole number, then 2 and 327,861 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 327,861 655,722
-1 -2 -327,861 -655,722

Now, we try dividing 655,722 by 3:

655,722 ÷ 3 = 218,574

If the quotient is a whole number, then 3 and 218,574 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 218,574 327,861 655,722
-1 -2 -3 -218,574 -327,861 -655,722

Let's try dividing by 4:

655,722 ÷ 4 = 163,930.5

If the quotient is a whole number, then 4 and 163,930.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 2 3 218,574 327,861 655,722
-1 -2 -3 -218,574 -327,861 655,722
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

1236918275412,14324,28636,42972,858109,287218,574327,861655,722
-1-2-3-6-9-18-27-54-12,143-24,286-36,429-72,858-109,287-218,574-327,861-655,722

More Examples

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